Question

the length of \\(\overline{ab}\\) is 5 units.
what is the length of the image of the line segment after a dilation with a scale factor of \\(\frac{5}{2}\\)?
enter your answer in simplest form in the box.
\\(\square\\) units

Explanation:

Step1: Recall dilation of length

When a line segment is dilated with a scale factor \( k \), the length of the image is the original length multiplied by \( k \). Here, original length of \( \overline{AB} \) is 5 units, scale factor \( k=\frac{5}{2} \).

Step2: Calculate the new length

Multiply the original length by the scale factor: \( 5\times\frac{5}{2}=\frac{25}{2} \).

Answer:

\(\frac{25}{2}\)